1. Field of the Invention
The present invention relates to a writing method and a writing apparatus. For example, it relates to an electron beam writing apparatus which can correct an exposure dose, and to a writing method thereof.
2. Description of Related Art
Microlithography technique that advances microminiaturization of semiconductor devices is extremely important and the unique process of forming a pattern in semiconductor manufacturing. In recent years, with high integration of large-scale integrated circuits (LSI), a line width (critical dimension) required for semiconductor device circuits is shrinking year by year. In order to form a desired circuit pattern on such semiconductor devices, a master or “original” pattern (also called a mask or a reticle) of high precision is needed. Then, the electron beam writing technique intrinsically having excellent resolution is used for producing such a highly precise master pattern.
FIG. 8 is a schematic diagram for explaining operations of a variable-shaped electron beam (EB) writing apparatus. As shown in the figure, the variable-shaped electron beam writing apparatus operates as follows: A first aperture plate 410 has a quadrangular such as rectangular opening 411 for shaping an electron beam 330. A second aperture plate 420 has a variable-shaped opening 421 for shaping the electron beam 330 that passed through the opening 411 into a desired rectangular shape. The electron beam 330 emitted from a charged particle source 430 and having passed through the opening 411 is deflected by a deflector to pass through a part of the variable-shaped opening 421 and thereby to irradiate a target workpiece or “sample” 340 mounted on a stage which continuously moves in one predetermined direction (e.g. x direction) during writing or “drawing”. In other words, a rectangle shaped as a result of passing through both the opening 411 and the variable-shaped opening 421 is written in the writing region of the target workpiece 340 on the stage. This method of forming a given shape by letting beams pass through both the opening 411 and the variable-shaped opening 421 is referred to as a VSB (Variable Shaped Beam) method.
When the electron beam irradiates a target workpiece, such as a mask, on which a resist film is applied, there are factors, such as a proximity effect and a fogging effect, that cause dimensional variation of the resist pattern. The proximity effect is a phenomenon where the electron beam emitted is reflected at the mask, thereby irradiating the resist again. The influence range of the proximity effect is about more than a dozen μm. By contrast, the fogging effect is a phenomenon where backward scattering electrons due to the proximity effect go out of the resist to scatter again at a lower part of the electron lens barrel and then reirradiate the mask, namely indicating a phenomenon of resist irradiation due to multiple scattering. The fogging effect affects a large region (from several mm to several cm) compared with the proximity effect. As one approach to highly accurately perform correction in calculating an influence of the fogging effect, there is disclosed a method of considering influence of the proximity effect (refer to, e.g., Japanese Patent Application Laid-open (JP-A) No. 2007-220728 (hereinafter to be referred to as Patent Literature 1)). Influence ranges of the fogging effect and the proximity effect greatly differ from each other intrinsically. Therefore, when calculating an influence of the proximity effect, the calculation is performed for each mesh region of a size sufficiently smaller than that used for calculating influence of the fogging effect. However, when calculating an influence of the fogging effect whose influence range is larger, it would take a long time if the influence of the proximity effect is calculated for each of all the regions each time. Then, according to the method of the Patent Literature 1, the mesh region for a proximity effect used for calculating a fogging effect is constituted by a mesh larger than an original mesh size for the proximity effect, and influence of the proximity effect used for calculating the fogging effect is separately computed for each mesh region for the proximity effect used for the fogging effect calculation.
In order to highly accurately perform writing with an electron beam, it is necessary to consider influence of the proximity effect and the fogging effect. A method for such consideration is disclosed in the Patent Literature 1. However, even when the mesh region for a proximity effect used for calculating a fogging effect is constituted by a mesh larger than an original mesh size for the proximity effect, it is still required to separately calculate the influence of the proximity effect used for fogging effect calculation, with respect to the entire region for the fogging effect calculation. Therefore, even though the time can be shortened compared with the case of separately performing calculation for each of all the regions by using an original mesh size for proximity effect, there still exists a problem that the time has not been yet sufficiently shortened.
Moreover, by using the method described in the Patent Literature 1, the case may exist where a proximity effect-corrected dose for fogging effect calculation is first computed with respect to the entire mask surface by using a mesh larger than an original mesh size for the proximity effect, and then further, a dose for fogging effect correction is computed, as a preprocessing prior to the writing operation. In that case, it is needed to previously prepare a computer resource necessary for creating a pattern area density map based on such a mesh size and calculating a dose for fogging effect correction, with respect to the entire mask surface. Then, it also becomes necessary to reduce such computer resource. Furthermore, even when calculating is performed as a preprocessing prior to the writing operation, it is desirable to reduce the previous calculation time in view of the entire writing time.